Problem: The sum of two angles is $95^\circ$. Angle 2 is $105^\circ$ smaller than $3$ times angle 1. What are the measures of the two angles in degrees?
Solution: Let $x$ equal the measure of angle 1 and $y$ equal the measure of angle 2. The system of equations is then: ${x+y = 95}$ ${y = 3x-105}$ Since we already have solved for $y$ in terms of $x$ , we can use substitution to solve for $x$ and $y$ Substitute ${3x-105}$ for $y$ in the first equation. ${x + }{(3x-105)}{= 95}$ Simplify and solve for $x$ $ x+3x - 105 = 95 $ $ 4x-105 = 95 $ $ 4x = 200 $ $ x = \dfrac{200}{4} $ ${x = 50}$ Now that you know ${x = 50}$ , plug it back into $ {y = 3x-105}$ to find $y$ ${y = 3}{(50)}{ - 105}$ $y = 150 - 105$ ${y = 45}$ You can also plug ${x = 50}$ into $ {x+y = 95}$ and get the same answer for $y$ ${(50)}{ + y = 95}$ ${y = 45}$ The measure of angle 1 is $50^\circ$ and the measure of angle 2 is $45^\circ$.